Answered: A leasing firm claims that the mean…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A leasing firm claims that the mean number of miles driven annually, µ, in its leased cans is less than 12460 miles. A random sample of 27 cars leased from this firm had a mean of 11839 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 1620 miles. Assume that the population is normally distributed. Is there support for the firm’s claim at the 0.05 level of significance?

The null hypothesis: H₀ : _____

The alternative hypothesis: H₁: ______

The type of test statistic: (choose one) _______

The value of the test statistic: ______

(round to at least three decimal places.)

The p-value: _____

(round to at least three decimal places.)

Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 12460 miles? Yes _____, NO ______

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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